Deterministic-Stochastic Subspace Identification of the Modal Parameters of a Machine Tool During Milling

Modal analysis is a standard tool for evaluating the dynamic behaviour of machine tools. Since the dynamic behaviour can differ for operating and analysis conditions, the use of operational modal analysis for machine tools has been researched over the last decade. However, the operation of a machine tool is a special case with respect to the excitation, as the excitation is both deterministic and stochastic in nature. Therefore, a perfect broadband excitation, which can be assumed to be white noise, does not occur in machine tools. This fact must be taken into account for the identification and makes the application of classical techniques of operational modal analysis to milling machines insufficient. The approach for identification of the modal parameters of a milling machine during machining, presented in the paper, is based on the deterministic-stochastic subspace identification, which can consider both the deterministic and the stochastic character of the excitation in machine tools better than the stochastic subspace identification being often used in operational modal analysis. For this purpose, the formulation of the input vector for a milling machine is crucial. The approach is developed with the help of simulations and demonstrated on a real machine tool. The results show an improvement compared to the stochastic subspace identification, which is visible in more clear stability diagrams and in a higher number of identified resonance frequencies.